It's about matching patterns.
The square of the binomial (x+a) is
... (x+a)² = x² +2ax +a²
The first two terms of this match the first two terms of the left side of your equation if a=2. When we complete the square, your equation will look like
... (x+2)² = (something)
When that is written in expanded form, it is
... x² +2·2x +2² = (something)
... x² +4x +4 = (something)
Right now, your equation has a constant term of 1 on the left. In the above pattern, we see that we need to have a constant term of 4 on the left. To get there, we need to add 3 to the equation.
... x² +4x +1 +3 = 10 +3 . . . . . we have added 3 to both sides
... x² +4x +4 = 13 . . . . . . . . . . simplified
... (x +2)² = 13 . . . . . . . . . . . . . the left side written as a square
The appropriate answer choice is
... A (x+2)² = 13